Liquid anomalies and Fragility of Supercooled Antimony

TL;DR

We address the long-standing gap in understanding the liquid and supercooled phases of elemental Sb by using a neural-network potential trained on DFT data to perform large-scale MD across broad temperatures and pressures. The study reveals water-like liquid anomalies, an emergence of A17-like local order, and a Two-State description, while also uncovering negative-pressure stabilization of the A17 phase and hints of a hidden liquid–liquid transition linked to ultrafast crystallization. A comprehensive thermodynamic and kinetic analysis shows Sb as a highly fragile liquid with no clear fragile-to-strong transition within accessible conditions, connecting liquid-state physics to the fast crystallization and amorphous stability of Sb-based PCMs. These findings position elemental Sb as a valuable model system for exploring the interplay between liquid-state anomalies, structural motifs, and phase-change behavior in PCM-relevant materials.

Abstract

Phase-change materials (PCMs) based on group IV, V, and VI elements, such as Ge, Sb, and Te, exhibit distinctive liquid-state features, including thermodynamic anomalies and unusual dynamical properties, which are believed to play a key role in their fast and reversible crystallization behavior. Antimony (Sb), a monoatomic PCM with ultrafast switching capabilities, stands out as the only elemental member of this group for which the properties of the liquid and supercooled states have so far remained unknown. In this work, we use large-scale molecular dynamics simulations with a neural network potential trained on first-principles data to investigate the liquid, supercooled, and amorphous phases of Sb across a broad pressure-temperature range. We uncover clear signatures of anomalous behavior, including a density maximum and non-monotonic thermodynamic response functions, and introduce a novel octahedral order parameter that captures the structural evolution of the liquid. Moreover, extrapolation of the viscosity to the glass transition, based on configurational and excess entropies, indicates that Sb is a highly fragile material. Our results present a compelling new case for the connection between the liquid-state properties of phase-change materials and their unique ability to combine high amorphous-phase stability with ultrafast crystallization.

Figures (26)

• Figure 1: $(P,T)$ phase diagram of Sb obtained with the AIMLP: The blue area indicates the region where we studied the liquid and amorphous phases, with 0.5 GPa resolved isobaric molecular dynamics. Darker blue areas highlight the regions of spontaneous crystallization and glassy dynamics within 4 ns, with calculated boundaries marked by small black circles. Crystals stability regions are colored in brown for the A17 phase and in yellow for A7. The melting curves are determined by direct coexistence simulations (dashed lines), to be compared with the experimental melting line of A7 (dash-dotted). The A17-A7 boundary (dotted line) is sketched between the crossing of melting curves and the enthalpy crossover at $T=0$ (large circles). The existence of a locus of density maxima in the liquid (stars) is a fingerprint of anomalous behavior. For subsequent molecular dynamics simulations at constant volume, we choose an isochore belonging to the lowest studied pressures, where crystallization is mostly suppressed ($\rho_m=6.12$ g/cm$^3$, red line with small circles).
• Figure 2: Crystallization and stable crystals. a) Spontaneous crystallization from the supercooled liquid at $\rho_m = 6.12~$g/cm³. In the upper panel we show the potential energy $U$ along the NVT trajectories. In the lower panel we display the survival probability $P(t)$, i.e. the probability not to nucleate within a time $t$, with poissonian error bars and exponential fits. b) Snapshots of partially crystallized samples, showing the formation of one or more nuclei of A17 in the [101] view (see the last panel). Liquid particles are visualized in light blue color with a smaller radius; crystal particles belonging to the main cluster(s) are colored in brown with larger radius and are connected by bonds. c) Atomic structure of A7 and A17 crystals in the conventional cells. We use different colors and decreasing thickness to represent the bonds with the first (brown), second (green) and third (blue, only for A17) groups of nearest neighbors (NNs). A7: side view slightly tilted from the [100] direction, highlighting the ABC stacking of $\beta$-antimonene pseudo-bilayers; a semitransparent polyhedron represents the distorted octahedral environment with the six NNs. A17: side views slightly tilted from the [100] direction, showing the "washboard" shape of the bilayers, and from [101], highlighting the AB stacking of symmetric-$\alpha$-antimonene and octahedral-like patterns; a semitransparent polyhedron represents the distorted defective octahedral environment with the five NNs.
• Figure 3: Anomalies in thermodynamic response functions and in structural data (markers), and two-states (TS) fit (solid lines) using Eq. \ref{['eq:two-states_S_highT']} and Eq. \ref{['eq:two-states_anomalyX']}. a) Mass density $\rho_m$ and b) potential energy $U$. c) Thermal expansion coefficient $\alpha_T=-1/\rho_m (\partial \rho_m / \partial T)_P$ and d) isobaric heat capacity $c_P=(\partial U/\partial T)_P$, both directly computed from the data in the top panels. e) Equilibrium fraction $\langle \xi \rangle$ of the low-temperature "anomalous" liquid, and f) isothermal compressibility $k_T=-1/\rho_m (\partial \rho_m / \partial P)_T$. The dashed lines in $\rho_m$ (panel a) and in $k_T$ (panel f) are the "background" high-temperature regime defined in Eq. \ref{['eq:two-states_anomalyX']}; they are fitted on the mass density for $T>T_\mathrm{min}^\mathrm{bkg}=850$ K, which is shown as a vertical line in panel a. The equilibrium fraction $\langle \xi \rangle$ is a structural measure of the anomaly, equal to the relative area of the secondary population in the distribution of the octahedral order parameter $q_\mathrm{oct}$ defined in Eq. \ref{['eq:q_oct']}.
• Figure 4: a) Isotherms of pressure $P$ and of potential energy $U$ as a function of mass density $\rho_m$, in the liquid and supercooled phases. Temperatures are 1500, 1200, 1000, 900, 800, 700, 600, 550, 500 K, after 10 K/ps cooling. We also report one glassy isotherm at 300 K for comparison. Data from the NVT ensemble with $N=216$ (small markers) and from the NPT ensemble with $N=4096$ (large markers) perfectly match. b) Structural analysis of liquid and crystal phases. Radial pair distribution $g(r)$, coordination number (CN), angular distribution $p(\theta)$, static structure factor $S(q)$, octahedral order parameter $q_\mathrm{oct}$ and Steinhardt order parameter $q_3$, of the liquid phase ("Liq.", from 900 K to 500 K) and of the crystal phases ("A7" and "A17", from 700 K to 300 K) at 6.12 g/cm$^3$, all with 100 K resolution. The radial cutoff for CN and $p(\theta)$ is $3.58~\text{\AA}$, shown as a vertical dashed line in the $g(r)$ panel. Liquid and A17 data are vertically shifted. Same colorbar as panel a.
• Figure 5: Low-temperature anomalies in the probability distribution of the octahedral order parameter $q_\mathrm{oct}$ in the liquid and supercooled phases, from 1500 K to 500 K. At low temperatures and for all pressures, the main peak shifts from $\sim 0.4$ to $\sim 0.5$ and a shoulder appears at $\sim 0.8$. The values of $q_\mathrm{oct}$ in the crystal phases, $q_\mathrm{oct}^\mathrm{A17}=0.755$ and $q_\mathrm{oct}^\mathrm{A7}=0.935$, are shown as vertical dashed lines. The results indicate that i) at low temperature the liquid becomes more ordered, and ii) a secondary type of liquid emerges, with local angular structure similar to that of A17 rather than A7.